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author | Holden Rohrer <hr@hrhr.dev> | 2020-04-14 22:42:59 -0400 |
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committer | Holden Rohrer <hr@hrhr.dev> | 2020-04-14 22:42:59 -0400 |
commit | 725f8b2b2fc250dcd6efdf8ba4108b196ed6d6b3 (patch) | |
tree | 3636ca5e1616d81510e22a871a0dfb7b994d400b /execsumm/document.tex | |
parent | 8269fa1fe084123e1360eaaba36f9d1f9311ac55 (diff) |
merged latex into plain tex
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-rw-r--r-- | execsumm/document.tex | 9 |
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diff --git a/execsumm/document.tex b/execsumm/document.tex index 85d2e87..2354637 100644 --- a/execsumm/document.tex +++ b/execsumm/document.tex @@ -78,6 +78,15 @@ should be a particular solution. This would allow usage of method of undetermined coefficients, which may be attempted, but variation of parameters will be used so that a general form for both systems with both complex and real eigenvalues may be found. +Essentially, the solution is ${\bf x} = c_1{\bf\lambda_1}(t) + +c_2{\bf \lambda_2}(t) + c_3{\bf \lambda_3}(t){\bf\lambda_p}(t)$, +where the particular solution ${\bf\lambda_p}(t)$ is: +$${\bf \lambda_p}(t) = {\bf X}(t)\int{\bf X^{-1}}(t){\bf g}(t)dt,$$ +where $\bf{X}(t)$ is the Fundamental matrix for the equation and +${\bf g}(t) = {1\over R_1} +\pmatrix{\omega\cos(\omega t)\cr + \omega\cos(\omega t)\cr + 0}.$ \section{Possible Generalization} |